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Second order elliptic equations in divergence form on unbounded domains. (Italian. English summary) Zbl 0799.35140

Summary: Let \(\Omega\) be a regular open set of \(\mathbb{R}^ n\), \(\mu\) a measure with compact support and \(L\) a second order elliptic operator in divergence form. If \(L\) is coercive we prove a theorem of existence and uniqueness for the solution of \(Lu=\mu\), \(u\in H_ 0^ 1+ H_ 0^{1,p'} (\Omega)\) where \(p'\) is the conjugate of \(p\in [n,\infty[\).

MSC:

35L15 Initial value problems for second-order hyperbolic equations
35R05 PDEs with low regular coefficients and/or low regular data
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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